A machine tool and a processing method are disclosed in DE 20 2009 013 899 U1. The machine of the prior art, which is constructed as a combined punch/laser machine, has a C-shaped machine frame having an upper frame leg at the free end of which a punching device and a laser processing device are arranged beside each other. The punching device and the laser processing device serve to process metal sheets which to this end are moved by a coordinate guide over a workpiece table on a lower frame leg of the C-shaped machine frame. For the punching processing of the metal sheet, an upper punch tool of the punching device carries out punching strokes along a vertical operating stroke axis. The laser processing device includes as a processing unit a laser processing head and as an accessory unit a shielding device. The laser processing head can be lifted along a vertical axis into a rest position remote from the workpiece and lowered into an operating position close to the workpiece. From the laser processing head which is located in the operating position, a laser processing beam is directed towards the metal sheet which is intended to be processed. The shielding device of the laser processing device can also be positioned in a vertical direction. In an operating position close to the workpiece, the shielding device serves to shield the processing site of the laser processing beam, which has been directed towards the relevant metal sheet by the laser processing head which has been lowered into the operating position, against the environment to in particular prevent in this manner laser radiation from emerging from the processing site of the laser processing beam into the environment. The operating position of the shielding device is defined in such a manner that a gap having a gap width of preferably approximately one millimeter remains between the lower side of the shielding device which is arranged in the operating position and the upper side of the metal sheet which is processed by the laser processing beam.